A gallery of finite subdivision rules

These images were produced using the finite subdivision rules software of Cannon-Floyd-Parry and the CirclePack software of Ken Stephenson. One starts with a finite subdivision rule R and an R-complex X that is topologically a disk (usually consisting of a single tile). Using the Cannon-Floyd-Parry program subdivide.c, one can rescursively subdivide X to get subdivisions R^n(X). One can then use the Cannon-Floyd-Parry program tilepack.c to write input script-files for Stephenson's program CirclePack. The output of CirclePack includes postscript files of the subdivisions. These postscript images have been used in several of our papers; many of them can be found in our coloring booklets.

The images here are computer colorings of these postscript images. Given a tile in the subdivision, its color is determined by its tile type and the tile types of its predecessor tiles in previous subdivisions. If there are three tile types, they are given the colors R, G, and B; the tile type of each of its predecessor tiles contributes to the color. For example, a tile is colored red if it has tile type 1 and all of its predecessors have tile type 1.

You can click on any image to download the (gzipped) postscript file that it was produced from. These are copyrighted images, and may not be used for commercial purposes without prior approval.

The diamond chains subdivision rule

The dodecahedral subdivision rule

A variant of the dodecahedral subdivision rule

The pentagonal subdivision rule

A rotationally symmetric subdivision rule with quadrilaterals and pentagons

A finite subdivision rule with hyperbolic and parabolic expansion complexes